Question

Sa se rezolve sistemele simetrice:

1) {x+y=4 {xy=3
2) {x+y=3 {xy=-10

Answer 1

1)
x+y=4
xy=3
Notam cu S=x+y si cu P=xy
S=4
P=3
FOrmam ecuatia :
t²-4t+3=0
Δ=b²-4ac
Δ=16-12=4=>√Δ=2
t1= 3 si t2= 1
S= { (3;1); (1; 3)}
2)x+y=3
   xy=-10
  S=3
P= -10
t²-3t-10=0
Δ=b²-4ac= 9+40= 49=>√Δ=7
t1= 5 t2= -2
S= { ( 5;-2); (-2;5)}